1. Field of the Invention
The present invention relates generally to Radon inversion processing, and more specifically to two-step Radon inversion processing where Radon data is sampled into .phi.-planes sample grids having independent local Radon origins. The invention is particularly useful in computed tomographic (CT) imaging apparatus that performs three-dimensional (3D) image reconstruction.
2. Description of the Background Art
Recently a system employing cone beam geometry has been developed for three-dimensional (3D) computed tomographic (CT) imaging that includes a cone beam x-ray source and a 2D area detector. An object to be imaged is scanned, preferably over a 360.degree. angular range and along its length, by any one of various methods wherein the position of the area detector is fixed relative to the source, and relative rotational and translational movement between the source and object provides the scanning (irradiation of the object by radiation energy). The cone beam approach for 3D CT has the potential to achieve 3D imaging in both medical and industrial applications with improved speed, as well as improved dose utilization when compared with conventional 3D CT apparatus (i.e., a stack of slices approach obtained using parallel or fan beam x-rays).
As a result of the relative movement of the cone beam source to a plurality of source positions (i.e., "views") along the scan path, the detector acquires a corresponding plurality of sets of cone beam projected measurement data (referred to hereinafter as measurement data), each set of measurement data being representative of x-ray attenuation caused by the object at a respective one of the source positions. After acquisition, the measurement data is processed for reconstructing a 3D image of the object.
As compared with the processing required for reconstructing an image when using an x-ray source supplying parallel or fan beams, the processing of the measurement data acquired when using a cone beam source is computationally much more complex. This is because when using a parallel or fan beam source, the measurement data is already directly representative of a 2D Radon transform of a cross-section of the object. However, this is not the case when using a cone beam source. Processing of the measurement data acquired using a cone beam source comprises:
1) conversion of the measurement data to Radon derivative data. This may be accomplished using the techniques described in U.S. Pat. No. 5,257,183 entitled METHOD AND APPARATUS FOR CONVERTING CONE BEAM X-RAY PROJECTION DATA TO PLANAR INTEGRAL AND RECONSTRUCTING A THREE-DIMENSIONAL COMPUTERIZED TOMOGRAPHY (CT) IMAGE OF AN OBJECT issued Oct. 26, 1993, hereby incorporated by reference,
2) conversion of the Radon derivative data to Radon data at polar grid points using, for example, the technique described in U.S. Pat. No. 5,446,776 entitled TOMOGRAPHY WITH GENERATION OF RADON DATA ON POLAR GRID POINTS issued Aug. 8, 1995, also hereby incorporated by reference, and
3) performing an inverse 3D Radon transformation of the Radon data using known techniques, such as those described in detail in the forenoted U.S. Pat. No. 5,257,183 for reconstructing image data that, when applied to a display, provides a view of the 3D CT image of the object.
Although the theory for exactly reconstructing an image using cone beam measurement data is generally known, such as from the U.S. patents noted above, a practical implementation of the processing turns out to be quite problematic. Not only is the amount of measurement data to be processed very large and rapidly acquired in accordance with a timing that is mainly determined by the geometry of the scan path, but the calculations required on the acquired data are quite complex. For example, if one decides to reconstruct an object with 200.times.200.times.200=8.10.sup.6 voxels (voxel=volume element of the object), for good quality one needs to obtain the object's 3-D Radon transform with a multiple amount (e.g., 4) of Radon samples, i.e., 32.10.sup.6 samples, and then perform the Radon inversion. The most computationally expensive part of the object reconstruction is the calculation of the Radon derivative data (step 1 noted above). As noted in the above U.S. patents, as well as in detail in U.S. Pat. No. 5,463,666 entitled HELICAL AND CIRCLE SCAN REGION OF INTEREST COMPUTERIZED TOMOGRAPHY issued Oct. 31, 1995, hereby incorporated by reference, for calculating the value of the Radon data at a given Radon sample point, it is typically necessary to process the measurement data acquired from several source positions, with the measurement data from each source position developing a contribution to the final value for that sample point by way of data combination. Thus one needs to calculate about 100.10.sup.6 line integral derivatives. Each line integral derivative requires the calculation of 200.10.sup.6 single line integrals, since one uses the difference between two closely spaced line integrals to calculate a single line integral derivative. However, before one can perform these line integral derivative calculations, one has to compute for each Radon sample which source positions will provide the measurement data that must be processed, and determine the lines on the measurement data along which the integration must be performed. These latter determinations involve highly nonlinear calculations and are therefore computationally costly. In order to compute the contributing source positions, one has to intersect the source scanning path with the Radon integration plane as explained in the forenoted U.S. Pat. No. 5,463,666. When using a spiral scan path, this requires the solution of transcendental equations, which are computationally expensive. Furthermore, in addition to determining the lines on the measurement data along which the integration must be performed, one also has to calculate the appropriate end points of those lines for data combination purposes and region-of-interest masking. The complexity of these above-noted calculations leads to severe bottlenecks in processing of the measurement data, so as to prevent rapid and efficient image reconstruction.
In U.S. patent application Ser. No. 08/940,924 entitled A PRE-CALCULATED HITLIST FOR REDUCING RUN-TIME PROCESSING OF AN EXACT CONE BEAM RECONSTRUCTION ALGORITHM, filed contemporaneously herewith, a method and apparatus is described in which before operation of a cone beam imaging apparatus for acquiring and processing of measurement data to reconstruct an image of an object, information required for processing of the acquired measurement data is pre-calculated and stored. The pre-calculated information is then used during the imaging operation of the cone beam apparatus for processing of the acquired measurement data to reconstruct an image of the object. The pre-calculated image reconstruction information is organized into what is referred to as a "hitlist". In general, the hitlist contains processing information that is determined primarily by geometric parameters of the imaging apparatus that are already predetermined during its imaging operation, such as the pitch and other parameters of the source/detector scan path, the object dimensions, the detector resolution, and a desired sampling of the scan path and the Radon space. The hitlist includes processing information indicating the correspondence between points in Radon space and the source positions that contribute thereto, parameters that define the line integrals that need to be calculated in the measurement data acquired at each of the source positions, as well as other information useful for image reconstruction processing.
Although calculation of the hitlist information is computationally expensive, since the information in the hitlist must be calculated anyway in order to process each set of the acquired measurement data during imaging operation of the apparatus, its pre-calculation provides a very significant speed-up of the run-time (image) processing of the measurement data and results in a greatly improved efficiency in the implementation of the image reconstruction algorithm. However, as described in more detail in the forenoted U.S. patent application Ser. No. 08/940,924, since hitlist information is required for each of the many points in Radon space that define the objects region of support, the size of the hitlist is actually quite large. For example, as previously noted, approximately 100.times.10.sup.6 line integral derivative calculation are required. If the image reconstruction processing information stored in the hitlist comprises 24 bytes to describe the processing for determining each Radon point, then 2.4 Gbytes of memory is required.
In U.S. patent application Ser. No. 08/940,489 entitled A REDUCTION OF HITLIST SIZE IN A SPIRAL CONE BEAM CT BY USE OF LOCAL RADON ORIGINS, filed contemporaneously herewith, a method and apparatus is described in which a symmetry is induced in the reconstruction processing so that reconstruction processing information contained in the hitlist and calculated on less than all of a set of vertically oriented co-axial .phi.-planes that partition the Radon space, is re-used for calculating Radon data for other ones of the .phi.-planes that partition the Radon space. The induced symmetry establishes a correspondence between the points in Radon space and the source positions, thereby allowing re-use of the reconstruction information calculated on only one of the .phi.-planes. In accordance with that invention, this is accomplished by establishing on each of successive ones of the .phi.-planes an independent local Radon origin. The Radon origin for each of the successive .phi.-planes are shifted an amount corresponding to an amount of z-axis shift that a projection of the spiral scan path experiences from its position in the immediately prior one of the successive .phi.-planes.
The present invention is directed to a method of processing Radon data having such independent Radon origins.